Chapter 3
Reflectance and transmittance of
light scattering scales stacked on
the wings of pierid butterflies
The colours of butterfly wings are determined by the structural as well as
pigmentary properties of the wing scales. Reflectance spectra of the wings of a
number of pierid butterfly species, specifically the Small White, Pieris rapae,
show that the long-wavelength reflectance of the scales in situ, on the wing, is
distinctly higher than that of single, isolated scales. An optical model explains
that this is due to multiple scattering on overlapping scales by treating the layers
of scales on both sides of the wing as a stack of incoherently scattering plates.
The model sheds new light on the adaptive significance and evolution of
butterfly wing patterns.
3.1 Introduction
Butterflies are generally strikingly coloured, due to light reflected by the wing
scales, which are arranged on the wing surface like shingles on a roof. The
reflected light commonly results from scattering on the scale structures, the
prominent longitudinal ridges and the connecting crossribs. A distinct colour is
observed when the scales contain a pigment that absorbs part of the scattered light
in a restricted spectral band. Butterflies thus combine physical and chemical
colouration methods. The scattered light usually is random and spectrally
indistinct, but interference can create striking, intense iridescent colours, as occurs
in the multilayers in the scales of the blue Morpho and other nymphalid butterflies
(Nijhout 1991; Brink & Lee 1999; Vukusic & Sambles 2003; Kinoshita &
Yoshioka 2005). Similar multilayers in the wing scales of male sulphurs cause a
strong UV reflectance (Ghiradella et al. 1972; Silberglied & Taylor 1973;
Butterfly wing scales - pigmentation and structural properties
Rutowski 1977). Photonic crystals in the scales of lycaenids (blues and
hairstreaks) result in a blue or green colour (Biro et al. 2003).
Many pierids apply a specific method of structural colouration in order to achieve
brightly-coloured wings. The scales are studded with beads (Yagi 1954;
Ghiradella 1998) that act as strong scatterers, which enhance the reflectance
(Stavenga et al. 2004; Rutowski et al. 2005). The wing scales of the yellow
sulphurs (Coliadinae) contain pigments that absorb in the ultraviolet as well as
blue wavelength ranges. The distinct yellow wing colour thus is due to the
combined effect of strong scattering in the long wavelength range and strong
absorption at the shorter wavelengths. The scales of male whites (Pierinae)
contain an ultraviolet-absorbing pigment, causing a low UV-reflectance, which is
well recognized by butterflies, but not by humans (Obara 1970; Obara & Majerus
2000).
The scales on each side of the wing are usually arranged in two layers, a layer of
ground scales and an overlapping layer of cover scales. In order to clarify the
optical consequences of the scale layering and their biological significance, we
have studied the optics of the butterfly wing scale assembly by measuring
reflectance and transmittance spectra of intact wings, of partially denuded wings,
and of single, isolated scales of pierid butterflies, and we have analyzed the
results with a simple model that treats the scales on the wing as a stack of layers,
assuming random scattering. We conclude that pierid butterflies realize their
bright wing colourations with stacks of strongly scattering scales, which contain
short wavelength absorbing pigments.
3.2 Materials and methods
Animals
All investigated butterflies belong to the family Pieridae. The Small White, Pieris
rapae, was obtained from a culture maintained by Dr J.J. van Loon, Entomology
department of the Agricultural University in Wageningen, the Netherlands. The
Autumn Leaf Vagrant, Eronia leda, was studied in the butterfly collection of the
latter department and in the Royal Museum of Central Africa, Brussels (curator
Dr U. Dall’Asta). The Common Jezabel, Delias nigrina, was obtained from Dr M.
Braby, Australian National University, Canberra.
Anatomy
The wing anatomy was
microscopical methods.
investigated
with
standard
scanning-electron-
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Spectrophotometry
Reflectance spectra of intact wings were measured with a reflection probe
connected to a fibre optic spectrometer (SD2000, Avantes, Eerbeek, the
Netherlands). Reflectance and transmittance spectra of intact as well as denuded
wings were measured with an integrating sphere (AvaSphere-50-Refl), connected
to the fibre optic spectrometer. Spectra of single scales were measured with a
home-built microspectrophotometer consisting of a Leitz Ortholux microscope
and the fibre optic spectrometer. A white reflectance standard (Spectralon,
Labsphere, North Sutton, NH, USA) served as a reference.
Modelling
The optical model that describes light propagation in a stack of layers assumes
non-coherent scattering. Each layer is characterized by reflectances r and s, and
transmittances t and u, depending on the direction of the incident light (Fig. 1).
The reflected and transmitted light fluxes in a two-layer stack with incident light
flux I1 from one side and I6 from the opposite side are then described by the
following set of equations (Fig. 1a):
I 2 = r1 I 1 + u1 I 4 ;
I 3 = t1 I 1 + s1 I 4 ;
I 4 = r2 I 3 + u 2 I 6 ;
I 5 = t 2 I 3 + s2 I 6
(1)
When the incident light flux is only from medium 1, then I 6 = 0 , or I 4 = r2 I 3 , so
that I 3 = t1 I 1 /(1 − s1 r2 ) and I 4 = t1 r2 I 1 /(1 − s1 r2 ) . The transmittance, T = I5/I1, and
reflectance, R = I2/I1, of the two layer stack then are:
T=
t 2 t1
1 − s1 r2
and
R = r1 +
t1u1 r2
.
1 − s1 r2
(2)
A stack consists in general of n layers. Equation (1) (where n = 2) can be
generalized as:
 I 2i 
 I 2i −1 
 I  = Ai  I
 ,
 2i +1 
 2i + 2 
with
r
Ai =  i
t i
ui 
,
s i 
for
i = 1...n ,
(3)
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Fig. 1. Diagrams of the
light flux in a pile of
plates. a Two rough layers,
1 and 2, each with
reflectances r and s and
transmittances t and u,
separate three media, 1 – 3.
b Layer i of a stack of n
layers separates media i
and i+1.
where layer i is characterized by matrix Ai (Fig. 1b). By introducing
τ i = I 2i +1 / I 2i −1 (for i = 1… n) and ρ i = I 2i / I 2i −1 (for i = 1… n + 1), Eq. (3) is
equivalent to:
τi =
ti
1 − s i ρ i +1
and
ρ i = ri + u i ρ i +1τ i = ri +
t i u i ρ i +1
.
1 − si ρ i +1
(4)
With only incident light I1, I2n+2 = 0 or ρn+1 = 0, which allows calculation of the
values of ρi and τi by recursion. Starting from i = n, it follows that τn = tn, ρn = rn,
τ n −1 = t n −1 /(1 − s n −1 ρ n ) , etc. The multilayer transmittance and reflectance are thus
directly derived from:
n
T = ∏τ i
and
R = ρ1 .
(5)
i =1
It is easy to see that Eq. (5) is identical to Eq. (2) for n = 2.
3.3 Results
3.3.1 Reflectance spectra of intact wings of two pierids
The male Autumn Leaf Vagrant, Eronia leda, provides a characteristic example
of the colouration of pierid butterflies (Fig. 2). The dorsal forewings are marked
by a prominent orange tip, which highly reflects ultraviolet light (Fig. 2, location
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Fig. 2. Reflectance spectra of the
dorsal forewing of the male
Autumn Leaf Vagrant, Eronia
leda (inset: upper – UV, lower –
RGB), measured with a fibre
optic spectrometer. Spectrum 1
is from the orange tip, which
exhibits a pronounced UV band,
due to interference reflectors in
the scale ridges. The orange
colour results from scattered
light, filtered by a pigment
absorbing in the UV, blue and
green
wavelength
range.
Spectrum 2 is from the dorsal
forewing area outside the orange
tip. The yellow colour results
from scattered light filtered by a
pigment absorbing in the UV and
blue wavelength range.
and spectrum 1). The remaining parts of the dorsal forewings and hindwings have
yellow colour (Fig. 2, location and spectrum 2). The orange as well as yellow
colours are due to pigments that selectively absorb short-wavelength light
scattered at the scale structures, the ridges, crossribs as well as the beads that
adorn the scales (Ghiradella 1998; Stavenga et al. 2004; Rutowski et al. 2005).
The high reflectance of the tips in the UV results from iridescence in the ridge
lamellae (Ghiradella et al. 1972; Silberglied & Taylor 1973; Rutowski 1977). The
ventral wings of the male Eronia leda are overall yellow, except for a minute UVreflecting spot in the ventral forewing. E. leda has a distinct sexual dichromatism,
as the female has pale yellow dorsal and ventral wings and only ventrally a few
scattered UV-reflecting spots.
The dorsal wings of the male Common Jezabel, Delias nigrina, have a simple
colour pattern (Fig. 3). The tips of the forewings are black, characteristic of a
melanin pigment, and they lack iridescence. The remaining parts of the dorsal
forewings and hindwings are white, due to strongly scattering scales. The
reflectance is low in the ultraviolet, due to a pigment that absorbs exclusively in
the UV (Fig. 3, spectra and locations 1-3). The ventral forewings and hindwings
are marked by yellow and red bands (spectra and locations 4 and 5) in a mainly
brown-black background (spectrum and location 6). Interestingly, the red bands
can be seen at the dorsal side as a slight red sheen, which is reflected in the
increase in reflectance in the wavelength range above 560 nm (spectra and
locations 1 and 3), corresponding to the wavelength range where the reflectance
of the red bands increases (spectrum and location 5).
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Fig. 3. Reflectance spectra of various parts of the wings of the male Common Jezabel, Delias
nigrina (inset: upper – dorsal, and lower – ventral), measured with a fibre optic spectrometer. The
reflectance of white areas is high and constant in the visible region (2). The low reflectance below
400 nm demonstrates that the white scales contain a UV absorbing pigment. The red sheen in 1 and
3 is due to bands of red scales at the ventral hindwing (5), which contain pterin pigments absorbing
throughout the visible wavelength region, except the red. The yellow bands in the ventral forewing
(4) contain UV and blue absorbing pterins. Spectrum 4 has a small foot between 400 and 470 nm
due to the contribution of white scales that occur in white spots at the dorsal side. The ventral wings
are mainly covered by brown-black scales, due to strongly absorbing melanin pigment (6).
This observation demonstrates that the ventral scales contribute to the dorsal wing
reflectance. The opposite also holds, namely the white spots in the tip of the
dorsal scales contribute to the ventral wing reflectance, as can be seen from the
slight foot at wavelengths above 400 nm in spectrum 4 of Fig. 3. The scales in the
white spots at the dorsal side add to the reflectance of the scales in the yellow
bands.
3.3.2 Reflectance and transmittance spectra of intact and denuded wings
of the Small White, Pieris rapae
We have attempted to assess the relative contributions of the scales to the
reflectance on both wing sides by considering the butterfly wing as a stack of
plates (Fig. 4), using the formalism described in the Methods. The reflectance was
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Fig. 4. Scanning electron microscopy
of wings of the Small White Pieris
rapae. a Rows of cover (c) and
ground (g) scales are stacked on the
wing substrate. b Side view of a cut
wing, showing cover and ground
scales on both dorsal and ventral
sides of the wing. Bar: 50 µm.
measured with an integrating sphere from both sides of intact wings (DWV,
VWD; Fig. 5a), from wings with scales removed on one side (DW, WD, WV,
VW; Fig. 5a, b) or from fully denuded wings (Wd, Wv; Fig. 5b). The reflectance
of the wings with scales is low in the UV and high at wavelengths above 450 nm.
The peak reflectance, around 500 nm, is about 0.6 for the intact wing, but the
reflectance of the scaleless wing is about 0.1, virtually independent of wavelength
(Fig. 5b). The overall spectral dependence of the transmittance, T(λ), resembles
that of the reflectance, R(λ); the transmittance is low in the UV and high in the
visible wavelength range (Fig. 5c, d).
Accordingly the absorptance, A(λ) = 1 - R(λ) - T(λ), is high in the ultraviolet and
negligible at the visible wavelengths (Fig. 5e, f). The scaleless wing absorbs only
slightly in the ultraviolet (Fig. 5f). The absorptance spectra of denuded wing and
wings with scales differ in shape, indicating that the pigments in wing substrate
and scales differ.
The wing covered by scales can be considered as a stack of layers, each with a
specific reflectance and transmittance, depending on the direction of the incident
light. The intact wing thus is a three layer stack, consisting of a layer of (partly
overlapping) scales at the dorsal side, D, the wing substrate, W, and the layer of
scales at the ventral side of the wing, V (Fig. 5). The reflectances r and s and the
transmittances t and u (Fig. 1) can be calculated for each of the three layers with
the formalism of the Methods. The wing reflectances rW and sW (Fig. 5b) as well
as the transmittances tW and uW (Fig. 5d) were measured directly, and further
spectral data were obtained for various two layer combinations, DW, WD, VW,
or VW, where only one layer of scales was present.
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Fig. 5. Reflectance (a, b) and transmittance (c, d) spectra measured from wings of the Small White
butterfly, Pieris rapae, in various conditions, together with the resulting absorptance spectra (e, f). The
measurements were performed with an integrating sphere. The wing was intact for the conditions DWV
and VWD, where D indicates the dorsal side of the wing, W is the wing substrate, and V is the ventral
side. The order of the letters indicates the direction of the incident light. For DW and WD, the wing
scales were removed at the ventral side, and for VW and WV, the wing scales were removed at the
dorsal side. For Wv and Wd, both dorsal and ventral scales were removed, and the incident light came
from the ventral (v) and dorsal side (d), respectively. The scales contain a strongly UV absorbing
pigment, resulting in a very low transmittance, or, a very high absorptance, in the ultraviolet. The wing
scales strongly scatter in the visible wavelength range. The wing reflectance is virtually constant
throughout the whole spectral range, with amplitude about 0.11 (b), and the wing substrate contains a
small amount of pigment that absorbs in the UV (f).
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The results for the dorsal scales are given in Fig. 6a and those for the ventral
scales in Fig. 6b. The absorptance for the D-scales with illumination from the
dorsal (d) side was calculated from aDd = 1 – rD – tD, and the absorptance with
illumination from the ventral (v) side from aDv = 1 – sD – uD (Fig. 6a). Similar
expressions hold for the V-scales (Fig. 6b).
Knowing the spectral data for all three layers (D, W, and V) allows calculation of
the reflectance and transmittance spectra of the intact wing, for example the three
layer stack DWV. This produced the calculated reflectance Rc = RDWV and
transmittance Tc = TDWV (Fig. 6c). The calculated spectra have a similar shape as
the measured spectra, Rm and Tm (Fig. 5a, c), but the calculated reflectance is too
small, and the calculated transmittance is too high (Fig. 6c). The corresponding
absorptances, Am and Ac, calculated from Am,c = 1 - Rm,c - Tm,c, closely agree.
3.3.3 Reflectance and transmittance spectra of single scales
Butterfly scales are more or less flat structures (Fig. 4), but they are quite
asymmetrical. The face toward the side of the wing (adwing) is rather smooth, but
the opposite side (abwing) is highly structured (inset Fig. 7b). We have measured
the reflectance of single scales, glued to the tip of a thin glass rod, with a
microspectrophotometer (Fig. 7a, b). We investigated both faces of ground and
cover scales from both the dorsal and ventral side of the scale. The reflectances of
both scale faces slightly differ, and the reflectance spectrum also depends
Fig. 6. Calculations of the reflectance, transmittance and absorptance of the dorsal (a) and ventral
(b) scale layers, using the data of Fig. 5 and the formalism described in the Methods. c The
reflectance and transmittance spectra measured from the intact wing (Fig. 5a and 5c, DWV), Rm and
Tm, are compared with the calculated spectra, Rc and Tc. The calculated reflectance (transmittance)
is somewhat smaller (larger) than the measured reflectance (transmittance). The absorptances are
calculated with Am,c = 1 - Rm,c - Tm,c.
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somewhat on the type of scale. The peak reflectance is roughly 0.3 in both cases,
at about 500 nm, but the reflectance in the UV is lower for the scale surface not
facing the wing (Fig. 7a).
The reflectance clearly depends on the scattering on the scale structures as well as
on the ultraviolet-absorbing pigment. To assess the amount of absorption in a
single scale, we measured the transmittance of various scales embedded in xylene,
an immersion fluid with a refractive index approximating that of insect cuticle
(Stavenga et al. 2004) (Fig. 7c). Fig. 7c also contains a transmittance spectrum
calculated from the absorptance spectra of Figs. 5 and 6. The calculation was
performed as follows. It was assumed that the absorption process in the layers can
be approximated with Lambert-Beer's law. The absorbance then is D(λ) = -log10[1
– A(λ)].
The absorptance spectra of Figs. 5e and 5f thus yielded absorbance spectra, which
after normalization appeared to be very similar. The mean of the normalized
absorbance spectra was therefore used to calculate a transmittance spectrum (Fig.
7c, bold curve, LB) with an amplitude in the ultraviolet of 0.15, about equal to the
transmittance in the UV of the immersed scales. The calculated transmittance
spectrum deviates from the measured transmittance spectra. Presumably xylene
does not fully annihilate the difference in refractive index of the scale structures
with that of the surrounding medium, which can be understood, because probably
the refractive index of pierid scales is not constant. The transmittance then
remains affected by scattering. Another reason for the deviation may be the
limited applicability of the model, which assumes perfectly diffuse light (see
Chapter 6).
3.3.4 Reflectance spectra of a stack of scales
We have used the model for a stack of reflecting and absorbing plates (Section
3.2) to calculate the reflectance of a multilayer of butterfly wing scales on the
wing. The measurements of Fig. 7 demonstrate that the reflectance slightly
depends on the type of scale (cover or ground). The reflectance also depends on
which side of the scales faces the incident beam. We nevertheless assumed a stack
of identical scales, with abwing (r) and adwing (s) reflectances equal to the mean
of the measured spectra (bold curves of Figs. 7a and 7b, respectively). The scale
transmittances t and u (Fig. 1) were calculated from t = 1 – r – a and u = 1 – s – a,
where the absorptance is a = 1 – tLB , with tLB the transmittance given by the bold
curve in Fig. 7c.
The resulting reflectance spectra of various stacks of scales on the wing are given
by Fig. 8. The reflectances of both sides of the denuded wing were assumed to be
equal to the average (W) of the two wing reflectance spectra given in Fig. 5b.
Spectrum SW of Fig. 8 presents the reflectance spectrum of a wing with one layer
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Fig. 7. Reflectance and transmittance spectra measured with a microspectrophotometer of single
cover and ground scales isolated from the dorsal as well as the ventral side of the forewing of a
male Pieris rapae. a Reflectance spectra measured abwing, that is, with the illumination coming
from the side of the ridges, which do not face the wing (see inset in b). The bold curve is the mean
of the measured curves. b Reflectance spectra measured adwing, that is, with the illumination
coming from the side of the scale that does not have ridges. The bold curve is the mean of the
measured curves. The maximum scale reflectance, both abwing and adwing, is roughly 0.3. In the
short wavelength range, the abwing reflectance (a) is more affected by the absorbing pterin pigment
than the adwing reflectance (b). c Transmittance spectra measured with the scales immersed in
xylene, to reduce scattering. The transmittance is low due to pterin pigment that absorbs strongly in
the UV. The transmittance at 375 nm is about 0.15, meaning a peak absorbance of about 0.8. The
bold curve (LB) is the transmittance spectrum calculated assuming Lambert-Beer’s law, taking the
absorption spectrum derived from the average normalized absorptance curves of Fig. 5e and f. The
distinct difference between the measured curves and the bold curve demonstrates that the
immersion fluid did not fully annihilate the refractive index differences. Inset b Transmission
electron microscopic image of a wing scale of Pieris rapae. The abwing side has prominent ridges
that are connected by crossribs. Beads adorn the latter structures. The adwing side is rather smooth,
although regularly spaced protrusions exist, resembling minor ridges (see Stavenga et al. 2004).
of scales on the side of the incident beam. At a glance it may seem strange that
the reflectance spectrum SW is lower than reflectance spectrum W in the UV. The
reason is the low reflectance as well as low transmittance of a single scale (S) at
short wavelengths (Fig. 7a), resulting in a low reflectance of the assembly, SW.
Spectrum SWS presents the case with one layer of scales on each side of the
wing, etc. The reflectance in the visible wavelength range steadily increases with
an increase in the number of scale layers, but the increment in reflectance
gradually decreases. The reflectance in the ultraviolet is completely governed by
the reflectance of the first layer of scales.
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Fig. 8. Reflectance spectra calculated for a set of identical scales stacked on the wing. The
reflectance of the scaleless wing (W) is the average of the spectra Wd and Wv of Fig. 5b. SW is the
reflectance calculated for a single layer of scales at the wing, with the reflectance r taken to be the
mean abwing reflectance of Fig. 5b and s is the mean adwing reflectance of Fig. 5b. The
illumination is from the side of the scale, S. SWS is the reflectance when a single scale exists on
both sides of the wing. SSWS has two layers of scales on the side of the wing from which the
illumination comes, and one layer of scales on the other side of the wing; and so on.
3.4 Discussion
Butterfly scales are extremely thin, in the order of hundreds of nanometers. Not
surprisingly, multilayer interference plays therefore a dominant role in many
cases of butterfly colouration. This is specifically the case in the cover scales on
the dorsal wings of male sulphur butterflies (Ghiradella et al. 1972; Silberglied &
Taylor 1973; Rutowski 1977; Rutowski et al. 2005), and in the tips of male pierid
butterflies of the Colotis group (Fig. 2).
Stokes (Stokes 1862) gave the first theoretical treatment of light reflected and
transmitted by a pile of plates where interference effects are negligible, which was
followed by a few more elaborate studies on stacks of thick layers (Smith 1926;
Baumeister et al. 1972). We have presented here a simple recursion procedure for
calculating the incoherent light flux in a stack of plates. For the modelling we
have assumed that the layers are sufficiently rough so that interference effects are
averaged out. The reflectance and transmittance spectra are then determined by
light scattering on the scale structures as well as by the absorbing pigments. Using
spectra measured on wings of the Small White butterfly (Fig. 5a-d) we have
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derived the reflectance and transmittance of the scale layers on each side of the
wing (Fig. 6a, b). The calculated spectra for the reflectance and transmittance of
an intact wing did not completely match the measured spectra, however (Fig. 6c).
This implies that the assumption of random scattering is not fully valid. In
addition, coherence may be not fully negligible. The general features are
nevertheless very clear. The wing reflectance of the Small White is not
exclusively determined by the scales on one side, but also the scales on the other
side of the wing contribute.
The maximal wing reflectance of the Small White is about 0.6 (Fig. 5a). This
corresponds to the reflectance value obtained for a stack of two scale layers on
each side of the wing (Fig. 8, SSWSS). Light and scanning electron microscopical
observations indeed show that in average about two scales overlap at the wings of
the Small White (Fig. 4). The wing reflectance of the Large White, Pieris
brassicae, can go up to 0.8, in agreement with our observation that stacks of
effectively three to four scales overlap in this species. Similarly, the dorsal wings
of the Common Jezabel (Fig. 3) have a high reflectance as well as several layers
of overlapping scales. In the latter case, the white reflectance is mainly due to
scales on the dorsal side of the wings, because most scales at the ventral side
contain a dense brown-black pigment. The scales in the striking red bands at the
ventral wing noticeably contribute to the dorsal reflectance in the longwavelength region (Fig. 3, spectra 1 and 3).
Enhancement of reflectance by multilayers of scales has been recently reported
for Morpho butterflies by Yoshioka and Kinoshita (2006b). They have used a
three layer wing model similar to that used above, but the procedure presented
here is easier and more generally applicable.
The wing reflectance is only a few percent in the ultraviolet for all cases
presented here. This is due to pigments absorbing in the short-wavelength range,
even in the white wings. Stacking several scales at the wing enhances the
reflectance at the long-wavelengths; meanwhile the short-wavelength reflectance
stays low. The pierid butterflies achieve a strong, saturated colour by combining a
distinct short-wavelength absorption with strong long-wavelength scattering,
which is realized by a multitude of nanometer-sized beads (Stavenga et al. 2004).
The strong colouration plays an important role in mutual, intersexual recognition
(Obara 1970). This will be especially the case where the male adds a strong
direction-depending iridescence in the ultraviolet (Ghiradella 1998; Rutowski et
al. 2005) to a yellow or orange pigment colour (Fig. 2).
In conclusion, we have demonstrated that the reflectance of butterfly wings
results from the coordinated effect of reflectances of single scale that are arranged
in stacks on the wings. This insight will be of considerable significance for
biologists working to understand the adaptive significance and evolution of
butterfly wing patterns.
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Acknowledgments
We thank three anonymous referees for constructive criticisms. Drs R. Rutowski
and H. Ghiradella read earlier versions of this paper. Financial support was given
by the EOARD (Grant 063027) and the EU via SYNTHESYS.
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